Leader selection for coherence in symmetric and asymmetric trees

This paper studies consensus dynamics in symmetric and asymmetric trees with leader selection under additive noise environment, which is characterized as leader–follower coherence determined by the spectrum. In order to compare the effect of the leader's positions on the coherence, we choose a tree-like network model and employ three different ways to assign the leaders. Based on the tree construction, we obtain exact solutions for the leader–follower coherence depending on the number of leaders and network parameters. We then show that the consensus in symmetric and asymmetric trees becomes better with an increasing number of leaders. When the number of leaders and network parameters satisfy certain conditions, the leader's positions and topological structures have a profound impact on the coherence.